Giving an author reading can be a daunting prospect, but actually it isn't. Here's why:
Remember when you were last in an audience, waiting to hear an author speak and read from their latest book. What were your expectations?
That you might have an enjoyable evening? That you might learn something interesting? That you might discover a new author to read? They probably weren't much more than that - you almost certainly weren't expecting to have the secrets of the universe revealed to you.
And what would you have been doing if you hadn't come to the reading?
Watched television? Gone out for a drink? Read a book? Got an early night? Again, I'm going guess that the alternatives weren't rivetingly exciting. Normal things, probably.
And what did you feel about the author?
If you didn't know them, probably not much - that they wouldn't be boring, maybe.
Now think about you, the author.
If this reading goes amazingly well, what is/are the best thing(s) that will happen?
Some people buy your book? An agent/publisher/famous author/fabulous person wants to meet up and gives you their number? The person you've been trying to chat up for ages is impressed?
All these things could lead somewhere good, but they're not exactly life-changing in themselves.
And now, if this reading goes incredibly badly, what is/are the worst thing(s) that will happen?
No one buys your book? No career-useful person approaches you? The person you've been trying to chat up for ages is still unimpressed?
In other words, you'll be at exactly the same place as you were if you hadn't done the reading.
Remember that it's all very low stakes. The audience don't expect much, and won't be that bothered if you don't even meet those expectations. And from your point of view, even if you forget your name and the title of your book (and I've done that on at least one occasion!) the stakes are very very low, both for you and for the audience.
The worst that can happen is nothing, and that's going to happen anyway if you don't do the reading. So you might as well stop being nervous and just get on with it.